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IGNOU SOLVED MEC-003/MEC- 103: QUANTITATIVE METHODS Assignment (TMA) 2019-2020 pdf
Course Code: MEC-003/ MEC-103
Asst. Code: MEC-003/103/TMA/2019-20
Total Marks: 100
Answer all the questions. Each question in Section A carried 20 marks while that in Section B carries 12 marks.
Section A
1. What is differential equation? How do you apply differential equations in Economics? Discuss the role of initial condition in solving a differential equation. If your objective is to examine the stability of equilibrium, show with the help of an example, how a second-order differential equation can address your concern.
2. (a) What is the normal probability distribution function? State its properties.
(b) The concentration of impurities in a semiconductor used in the production of microprocessors for computer is a normally distributed random variable with mean 127 parts per million (ppm) and standard deviation 22 parts per million. A semiconductor is acceptable only if its concentration of impurities is below 150 parts per million. What is the proportion of the semiconductors that are acceptable for use? (The area under the standard normal curve for the value of Z=1.05 is 0.3531)
Section B
3. Explain the relevant considerations of making a choice between one-tailed and two-tailed tests. How would you determine the level of significance in the above tests?
4. How would you determine linear dependence of a matrix? Define the rank of a matrix in terms of its linear independence.
5. A monopolist’s demand curve is given by P = 100 – 2q.
(a) Find the marginal revenue function.
(b) At what price is marginal revenue zero?
(c) What is the relationship between the slopes of the average revenue and marginal revenue curves?
6. Solve the following linear programming problem in x1 and x2.
Min C = 0.6x1 + x2
Sub to 10 x1 + 4 x2 ≥ 20
5 x1 + 5 x2 ≥ 20
2 x1 + 6 x2 ≥ 12
x1 , and x2 ≥ 0.
7. Write short notes on the following:
(i) Eigen vectors and Eigen values
(ii) Taylor’s expansion
(iii) Mixed strategy equilibrium
(iv) Kuhn-Tucker condition
6. Solve the following linear programming problem in x1 and x2.
Min C = 0.6x1 + x2
Sub to 10 x1 + 4 x2 ≥ 20
5 x1 + 5 x2 ≥ 20
2 x1 + 6 x2 ≥ 12
x1 , and x2 ≥ 0.
7. Write short notes on the following:
(i) Eigen vectors and Eigen values
(ii) Taylor’s expansion
(iii) Mixed strategy equilibrium
(iv) Kuhn-Tucker condition
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